As long as \(Q_t\)  remains close to \(Q\)  we expect that \(Y_t\)  is a random walk with drift approximately \(Q\) .
So in particular, for our setting of \(Q<0\) , we expect that the random walk will quickly return to 0.
Thus, we shall start by showing that the drift parameter \(Q_t\)  is indeed close to \(Q\)  with high probability.
For this we shall use the following formulation of the Azuma-Hoeffding inequality (see [1]}).
